Noise cancellation systems are used in various applications ranging from telephony to acoustic noise cancellation in communication headsets. There are, however, significant difficulties in implementing such stable, high performance noise cancellation systems.
In the majority of adaptive systems, the well-known LMS algorithm is used to perform the noise cancellation. This algorithm, however, lacks stability in the presence of inadequate excitation, non-stationary noise fields, low signal-to-noise ratio, or finite precision effects due to numerical computations. This has resulted in many variations to the standard LMS algorithm, none of which provide satisfactory performance over a range of noise parameters.
Among the variations, the leaky LMS algorithm has received significant attention. The leaky LMS algorithm, first proposed by Gitlin et al. introduces a fixed leakage parameter that improves stability and robustness. However, the leakage parameter improves stability at a significant expense to noise reduction performance.
Thus, the current state-of-the-art LMS algorithms must tradeoff stability and performance through manual selection of tuning parameters, such as the leakage parameter. In such noise cancellation systems, a constant, manually selected tuning parameter cannot provide optimized stability and performance for a wide range of different types of noise sources such as deterministic, tonal noise, stationary random noise, and highly nonstationary noise with impulsive content, nor adapt to highly variable and large differences in the dynamic ranges evident in real-world noise environments. Hence, “worst case”, i.e., highly variable, nonstationary noise environment scenarios must be used to select tuning parameters, resulting in substantial degradation of noise reduction performance over a full range of noise fields.
Presently, commercial active noise reduction (ANR) technology uses feedback control to reduce unwanted sound. A feedback topology is shown in FIG. 16. Here, the measured error signal ek is minimized through an infinite impulse response feedback compensator designed using traditional frequency-domain methods. The feedback controller seeks to force the phase between the output signal and the error signal equal to −180 degrees for as much as the ANR frequency band as possible. In active noise control, a high-gain control law is required to achieve this objective and to maximum ANR performance. However, a high-gain control law leaves inadequate stability margins, and such systems destabilize easily in practice, as the transfer function of the system can vary substantially with environmental conditions. In order to provide adequate stability margins, ANR performance is sacrificed, thus present feedback technology exhibits narrowband performance and “spillover” or creation of noise outside of the ANR band. Present commercial technology implements feedback control using analog circuitry.